The number of spanning trees in circulant graphs
نویسندگان
چکیده
منابع مشابه
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متن کاملFurther analysis of the number of spanning trees in circulant graphs
Let 1 s1<s2< · · ·<sk n/2 be given integers. An undirected even-valent circulant graph, C12k n , has n vertices 0, 1, 2, . . ., n− 1, and for each si (1 i k) and j (0 j n− 1) there is an edge between j and j + si (mod n). Let T (C12k n ) stand for the number of spanning trees of C12k n . For this special class of graphs, a general and most recent result, which is obtained in [Y.P. Zhang, X.Yong...
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Circulant graphs are an extremely well-studied subclass of regular graphs, partially because they model many practical computer network topologies. It has long been known that the number of spanning trees in n-node circulant graphs with constant jumps satisfies a recurrence relation in n. For the non-constant-jump case, i.e., where some jump sizes can be functions of the graph size, only a few ...
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In this paper, we develop a new method to produce explicit formulas for the number τ(n) of spanning trees in the undirected circulant graphs Cn(s1, s2, . . . , sk) and C2n(s1, s2, . . . , sk, n). Also, we prove that in both cases the number of spanning trees can be represented in the form τ(n) = p n a(n), where a(n) is an integer sequence and p is a prescribed natural number depending only of p...
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 223 شماره
صفحات -
تاریخ انتشار 2000